Mathematische Annalen

, Volume 273, Issue 3, pp 353–374 | Cite as

Cohomology of infinitesimal and discrete groups

  • Eric M. Friedlander
  • Brian J. Parshall
Article

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References

  1. 1.
    Andersen, H.H., Jantzen, J.C.: Cohomology of induced representations for algebraic groups Math. Ann.269, 487–525 (1984)Google Scholar
  2. 2.
    Borel, A.: Chevalley groups. In: Seminar on algebraic groups and related finite groups. Lect. Notes Math. 131. Berlin, Heidelberg, New York: Springer 1970Google Scholar
  3. 3.
    Bourbaki, N.: Groupes et algèbres de Lie. I. Paris: Hermann 1971Google Scholar
  4. 4.
    Bourbaki, N.: Groupes et algèbres de Lie. IV–VI. Paris: Hermann 1968Google Scholar
  5. 5.
    Carter, R.: Simple groups of Lie type. New York: Wiley 1972Google Scholar
  6. 6.
    Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras, and representations. J. Algebra63, 98–123 (1980)Google Scholar
  7. 7.
    Cline, E., Patshall, B., Scott, L.: A Mackey imprimitivity theory for algebraic groups Math. Z.182, 447–471 (1983)Google Scholar
  8. 8.
    Cline, E., Parshall, B., Scott, L.: On injective modules for infinitesimal algebraic groups. I. J. London Math. Soc. (2)31, 211–291 (1985)Google Scholar
  9. 9.
    Cline, E., Parshall, B., Scott, L., Kallen, W. van der: Rational and generic cohomology. Invent. Math.39, 143–163 (1977)Google Scholar
  10. 10.
    Donkin, S.: Rational representations of algebraic groups: Tensor products and filtrations. Lec. Notes Math. 1140. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  11. 11.
    Evens, L.: The cohomology ring of a finite group. Trans. Am. Math. Soc.101, 224–239 (1961)Google Scholar
  12. 12.
    Dwyer, W.: Homology of integral upper-triangular matrices. Proc. A.M.S.84, 523–528 (1985)Google Scholar
  13. 13.
    Friedlander, E., Parshall, B.: Etale cohomology of reductive groups. AlgebraicK-theory, Evanston 1980. Lect. Notes Math. 854. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  14. 14.
    Friedlander, E., Parshall, B.: Cohomology of algebraic and related finite groups. Invent. Math.74, 85–117 (1983)Google Scholar
  15. 15.
    Friedlander, E., Parshall, B.: Cohomology of Lie algebras and algebraic groups. Am. J. Math. (to appear)Google Scholar
  16. 16.
    Friedlander, E., Parshall, B.: Limits of infinitesimal group cohomology. To appear in Annals of Math. StudiesGoogle Scholar
  17. 17.
    Greub, W., Halperin, S., Vanstone, R.: Connections, curvature, and cohomology. III. London, New York: Academic Press 1976Google Scholar
  18. 18.
    Hilton, P., Stammbach, U.: A course in homological algebra. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  19. 19.
    Hochschild, G.: Cohomology of restricted Lie algebras. Am. J. Math.76, 555–580 (1954)Google Scholar
  20. 20.
    Humphreys, J.: Modular representations of classical Lie algebras and semisimple groups. J. Algebra19, 51–79 (1971)Google Scholar
  21. 21.
    Jantzen, J.C.: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne. J. Reine Angew. Math.317, 159–199 (1980)Google Scholar
  22. 22.
    Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, 329–387 (1961)Google Scholar
  23. 23.
    Lambe, L., Priddy, S.: Cohomology of nilmanifolds and torsion free, nilpotent groups. Trans. Am. Math. Soc.273, 39–55 (1982)Google Scholar
  24. 24.
    May, J.P.: The cohomology of restricted Lie algebras and of Hopf algebras. J. Algebra3, 123–146 (1966)Google Scholar
  25. 25.
    Nomizu, K.: On the cohomology of compact homogeneous spaces of nilpotent Lie groups. Ann. Math.59, 531–538 (1954)Google Scholar
  26. 26.
    Quillen, D.: On the associated graded ring of a group ring. J. Algebra10, 411–418 (1968)Google Scholar
  27. 27.
    Warner, G.: Harmonic analysis on semisimple Lie groups. I. Berlin, Heidelberg, New York: Springer 1972Google Scholar
  28. 28.
    Wilkerson, C.: The cohomology algebras of finite dimensional Hopf algebras. Trans. Am. Math. Soc.264, 137–150 (1981)Google Scholar
  29. 29.
    Zeeman, E.: A proof of the comparison theorem for spectral sequences. Proc. Camb. Phil. Soc.59, 57–62 (1957)Google Scholar
  30. 30.
    Koppinen, M.: Decomposing and lifting hyperalgebras. Turku thesis (1983)Google Scholar
  31. 31.
    Brown, K., Dror, E.: The Artin-Rees property in homology. Isr. J. Math.22, 93–109 (1975)Google Scholar
  32. 32.
    Grünefelder, L.: On the homology of filtered and graded rings. J. Pure App. Algebra14, 21–37 (1979)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Eric M. Friedlander
    • 1
  • Brian J. Parshall
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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